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簡諧運動
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重力與軌道
Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.
Start Gravity and Orbits物理62 concepts
力學
15 concepts物理力學
動量與衝量
用定時力脈衝推動小車，觀察動量、衝量與力對時間的面積如何緊扣同一次運動、讀值與圖表。
物理力學
動量守恆
看兩輛車在同一個受限內部互動中如何交換動量，並理解總動量為何保持不變，而各自速度與質心運動一起更新。
物理力學
碰撞
讓兩輛小車在同一條誠實的軌道上碰撞，保持總動量可見，並看彈性、質量與入射速度如何決定反彈或黏在一起的結果。
物理力學
拋體運動
發射一個拋體，觀察軌跡如何形成，並把射程、最高點與分量運動直接連到發射設定。
運動與圓周運動 - 2/3
A strong first concept for opening the catalog without committing to a full track.
Open 拋體物理力學
重力勢與重力勢能
看單一來源質量如何形成負值的勢阱，比較勢與勢能隨距離的變化，並在同一個即時模型中把 φ 的下降趨勢連到重力場。
重力與軌道 - 2/5
物理力學
克卜勒第三定律與軌道週期
比較繞同一來源質量的圓形軌道，理解較大軌道為何需要更長時間：路徑更長、圓周速度更低，而同一個即時模型讓週期定律清楚可見。
重力與軌道 - 4/5
流體
5 concepts熱力學
4 concepts物理熱力學
理想氣體定律與氣體分子動理論
在同一個受限粒子箱中連結壓力、體積、溫度與粒子數，然後把這些壓力變化再讀回粒子速度與碰壁頻率的改變。
熱力學與動力學理論 - 2/4
物理熱力學
比熱與相變
看看同樣的能量脈衝為何會讓不同材料升溫幅度不同，以及為何相變平台能在不改變溫度的情況下吸收或釋放能量。
熱力學與動力學理論 - 4/4
物理熱力學
溫度與內能
比較粒子的平均運動與整體樣本的能量，改變物質量與加熱，並在同一個熱學實驗台上看相變平台如何打破只看溫度的直覺。
熱力學與動力學理論 - 1/4
A strong first concept for opening the catalog without committing to a full track.
Open Temperature vs U電學
6 concepts電磁學
5 concepts物理電磁學
電磁波
看變化中的電場與磁場如何一起向右傳播成為同一個波，讓局部場對、源到探針的延遲與傳播線索都留在同一個小型即時舞台。
物理電磁學
磁場對運動電荷與電流的作用力
讓一個運動電荷穿過均勻磁場，再與同方向電流段比較，並在同一個受限即時舞台上連結力的方向、軌跡彎曲與電流受力。
Magnetism - 3/3
物理電磁學
馬克士威方程組綜合
理解每條馬克士威方程的物理意義、來源與環流的差別，以及為何電場與磁場的相互變化把電、磁與光統一起來。
Optics
10 concepts物理Optics
光作為電磁波
把電磁波連到可見光、顏色、頻率與更廣的光譜，同時用同一個小型舞台把光譜軌、場對示意與介質相關波長變化綁在一起。
物理Optics
偏振
用同一個小型偏振片實驗台理解偏振是橫波方向的故事，觀察角度不匹配如何決定透射光，以及理想偏振片如何把未偏振光整理成單一軸向。
Wave Optics - 1/5
物理Optics
折射／斯涅爾定律
看一道光線穿過介面，把折射率與速度變化連起來，並理解斯涅爾定律如何決定折射角、彎折方向與臨界角極限。
物理Optics
色散／折射率與顏色
用一個小型薄稜鏡實驗台看折射率如何依波長改變、不同顏色為何折得不同，以及受限的稜鏡模型如何分開顏色而不變成完整光譜學系統。
Wave Optics - 4/5
物理Optics
全內反射
把光線從高折射率介質推向低折射率邊界，觀察臨界角如何出現，並看同一張即時圖如何從普通折射切換到完全內反射。
物理Optics
鏡面成像
用平面鏡、凹面鏡與凸面鏡在同一張即時光線圖上追蹤等角反射、有號像距與放大率。
物理Optics
透鏡成像
透過主光線追蹤會聚與發散透鏡，將有號薄透鏡方程直接對應到圖像，並看像距與放大率如何回應同一組物體設定。
物理Optics
光學解析度／成像極限
讓兩個接近的點光源通過有限孔徑成像，理解繞射、波長與孔徑直徑如何限制光學系統分辨它們的能力。
Wave Optics - 5/5
現代物理
5 concepts物理現代物理
光電效應
用一個小型光源到金屬的實驗台理解為何光頻率決定電子是否逸出、為何只靠強度無法跨越閾值，以及截止電壓如何誠實讀出電子能量。
現代物理 - 1/5
物理現代物理
德布羅意物質波
用一個小型物質波實驗台理解粒子動量如何決定波長、為何較重或較快的粒子有更短波長，以及整數圈適配如何成為早期量子行為的受限橋樑。
現代物理 - 3/5
Oscillations
11 concepts物理Oscillations
簡諧運動
在同一個反覆系統中，從位移到加速度再回到位移，直接看懂週期性運動。
振盪與能量 - 1/3波動入門 - 1/9
A strong first concept for opening the catalog without committing to a full track.
Open 簡諧物理Oscillations
都卜勒效應
看著移動聲源在前方壓縮、後方拉開波前，並理解聲源與觀察者運動如何共同改變聽到的音高。
波動入門 - 6/9聲音與聲學 - 4/5
物理Oscillations
音高、頻率與響度／強度
在同一個小型聲學實驗台上分清音高與頻率、響度與振幅／強度，以及探針延遲與訊源聲音本身。
波動入門 - 4/9聲音與聲學 - 2/5
物理Oscillations
聲波與縱波運動
把聲音視為縱波，讓介質微粒運動、疏密變化、探針讀值與能量傳遞都留在同一個介質優先的實驗台上。
波動入門 - 3/9聲音與聲學 - 1/5
物理Oscillations
空氣柱共鳴／開管與閉管
在同一個空氣柱中比較開管與閉管邊界條件，讓駐波形狀、偶次諧波缺失、探針運動與壓力線索都綁在同一個共鳴狀態。
波動入門 - 9/9聲音與聲學 - 5/5
Resonance
1 concepts數學16 concepts
函數
3 concepts微積分
4 concepts數學微積分
Derivative as Slope / Local Rate of Change
Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.
函數與變化 - 4/6
數學微積分
極限與連續／逼近某個值
從左與右逼近同一個目標點，比較極限高度與函數實際值，並在同一張圖上對照連續、可去間斷、跳躍與發散行為。
函數與變化 - 5/6
數學微積分
最佳化／最大值、最小值與限制
在固定周長下改變矩形寬度，觀察面積曲線如何達到峰值，並用局部斜率看出正方形為何是最佳受限形狀。
向量
3 concepts數學向量
矩陣變換／伸縮、剪切、反射
讓同一個 2×2 矩陣同時作用在網格、基底向量與範例圖形上，使平面變換保持可視化而不只是符號。
數學向量
內積／夾角與投影
把兩個向量、它們的夾角、其中一個投影到另一個的有號分量，以及內積一起顯示，讓對齊程度從幾何上變得清楚。
複數與參數運動
6 concepts數學複數與參數運動
參數曲線／由方程描述運動
把 x(t)、y(t)、描出的路徑與移動點同時顯示，清楚分開形狀本身與沿著曲線前進的方式。
複數與參數運動 - 6/6
數學複數與參數運動
單位圓／由旋轉理解正弦與餘弦
把旋轉點、x/y 投影與正弦餘弦曲線連在一起，讓單位圓成為這兩個函數的即時來源。
複數與參數運動 - 2/6
化學9 concepts
反應速率與平衡
2 concepts化學計量與產率
3 concepts溶液與 pH
4 concepts電腦科學6 concepts
演算法與搜尋
6 concepts電腦科學演算法與搜尋
排序與演算法取捨
把排序看成對即時列表的可見工作，使輸入順序、比較次數與寫入動作都保持具體，而不是只剩最後答案。
演算法與搜尋基礎 - 1/6
電腦科學演算法與搜尋
二分搜尋／把搜尋空間減半
把有序列表、low-mid-high 標記與不斷縮小的區間一起留在視野中，讓二分搜尋變得可視，而不只是流程步驟。
演算法與搜尋基礎 - 2/6
電腦科學演算法與搜尋
圖上的前沿與已訪狀態
把重複略過、等待中的前沿節點與已展開節點一起顯示，讓循環處理看起來像誠實的狀態管理。
演算法與搜尋基礎 - 6/6
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Open another route only when you need a different shape.
Subject pages, topic pages, starter tracks, and guided collections stay available, but they stay out of the way until you ask for them.
Subjects
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Subjects
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Newer subject branch3 topics3 starter tracks
化學
從反應速率、平衡、化學計量與溶液酸鹼等模擬主題進入化學內容。
Fastest honest route
反應速率與平衡 is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.
Newer subject branch1 topics1 starter tracks
電腦科學
從排序、搜尋與圖遍歷等演算法主題進入目前的電腦科學內容。
Fastest honest route
演算法與搜尋基礎 is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.
Subject directory
Open subject directorySubject8 topics62 concepts
物理
透過運動、波動、場、電路與現代物理的即時實驗台進入目前的物理內容。
運動與圓周運動 is the clearest bounded first route.
Subject4 topics16 concepts
數學
以圖像變換、函數、複數平面、三角與向量等互動主題進入數學內容。
函數與變化 is the clearest bounded first route.
Subject3 topics9 concepts
化學
從反應速率、平衡、化學計量與溶液酸鹼等模擬主題進入化學內容。
反應速率與平衡 is the clearest bounded first route.
Subject1 topics6 concepts
電腦科學
從排序、搜尋與圖遍歷等演算法主題進入目前的電腦科學內容。
演算法與搜尋基礎 is the clearest bounded first route.
Guided starts
Show tracks and guided starts
19 tracks and 10 guided collections stay here when you want sequence instead of a free browse.
Guided starts
Show tracks and guided starts
19 tracks and 10 guided collections stay here when you want sequence instead of a free browse.
Starter tracks
Stay in libraryStarter track3 concepts75 min
運動與圓周運動
Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.
Starts with 向量與分量 across 3 concepts.
Starter track5 concepts130 min
轉動力學
Start with torque as the turning effect of force, use centre of mass and support region for static balance, then carry the same rotational language into moment of inertia, rolling motion, and angular momentum.
Starts with 力矩 across 5 concepts.
Starter track5 concepts135 min
重力與軌道
Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.
Starts with 重力場 across 5 concepts.
Starter track3 concepts80 min
振盪與能量
Build from one clean oscillator to energy exchange and then to driven resonance, so the same system grows without changing its core ideas.
Starts with 簡諧運動 across 3 concepts.
Starter track5 concepts145 min
流體與壓力
Start with pressure in a resting fluid, then carry that same branch through continuity, Bernoulli, buoyancy, and drag-limited motion.
Starts with 壓力與靜水壓 across 5 concepts.
Starter track9 concepts230 min
波動入門
Use oscillation as the entry point, lock down wave speed and wavelength, carry that into longitudinal sound and pitch-versus-loudness cues, add beats as the nearby-frequency superposition bridge, then move into Doppler shifts, interference, standing-wave patterns, and open-vs-closed air-column resonance without losing the live connection between motion and graph.
Starts with 簡諧運動 across 9 concepts.
Starter track4 concepts125 min
熱力學與動力學理論
Start with temperature-versus-internal-energy bookkeeping, reuse that particle story for gas pressure, then follow energy transfer into heating curves and phase-change shelves.
Starts with 溫度與內能 across 4 concepts.
Starter track6 concepts160 min
電學入門
Start with source charges and voltage, then carry that same circuit story into current, power, branch behavior, and equivalent resistance.
Starts with 電場 across 6 concepts.
Starter track3 concepts80 min
Magnetism
Start with current-made magnetic fields, turn changing flux into induced emf with Faraday and Lenz, and then reuse that same field direction story to explain magnetic force on charges and currents.
Starts with 磁場 across 3 concepts.
Starter track5 concepts120 min
聲音與聲學
Stay on the sound branch long enough that longitudinal motion, pitch-versus-loudness cues, beats, Doppler shifts, and open-vs-closed air-column resonance feel like one acoustics path instead of isolated pages.
Starts with 聲波與縱波運動 across 5 concepts.
Starter track5 concepts145 min
Wave Optics
Follow the bounded wave-optics branch from polarization into diffraction, double-slit interference, color-dependent refraction, and imaging limits so the newer optics pages read like one compact path instead of isolated stops.
Starts with 偏振 across 5 concepts.
Starter track5 concepts150 min
現代物理
Follow the bounded modern-physics branch from threshold emission into line spectra, matter waves, the Bohr hydrogen model, and half-life so the new concept set reads like one path instead of five isolated pages.
Starts with 光電效應 across 5 concepts.
Starter track6 concepts139 min
函數與變化
Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.
Starts with 圖像變換 across 6 concepts.
Starter track6 concepts140 min
複數與參數運動
Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).
Starts with 複平面上的複數 across 6 concepts.
Starter track2 concepts50 min
向量與運動橋接
Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.
Starts with 二維向量 across 2 concepts.
Starter track2 concepts50 min
反應速率與平衡
Start with successful collisions setting reaction rate, then reuse the same chemistry language inside a reversible system that re-balances after a disturbance.
Starts with 反應速率／碰撞理論 across 2 concepts.
Starter track3 concepts72 min
化學計量與產率
Start with one visible reaction recipe, use the lower batch cap to identify the limiting reagent, and then compare actual output with the same theoretical marker.
Starts with 化學計量比與反應配方批次 across 3 concepts.
Starter track4 concepts95 min
溶液與 pH
Start with concentration in one beaker, add solubility limits and saturation, then reuse that same solution language to read pH, buffers, and neutralization.
Starts with 濃度與稀釋 across 4 concepts.
Starter track6 concepts138 min
演算法與搜尋基礎
Start with visible list work, reuse that search language for binary search, and then carry the branch into one live graph bench for adjacency, BFS, DFS, and visited-state behavior.
Starts with 排序與演算法取捨 across 6 concepts.
Guided collections
Open guided collectionsLesson set4 steps9 concepts
Waves Evidence Loop
Use one topic route, one starter track, and one focused challenge so the wave story stays bounded for a teacher-led lesson block.
A sequenced set of 9 concepts.
Lesson set6 steps6 concepts
Electricity Bridge Lesson Set
Move from field cause to voltage to the first full electricity track without leaving the current concept, topic, and challenge surfaces.
A sequenced set of 6 concepts.
Playlist5 steps11 concepts
Electricity to Magnetism Bridge
Use the existing electricity recap, magnetic starter track, and Maxwell capstone surfaces to move into electromagnetism without turning the branch into a full LMS sequence.
A sequenced set of 11 concepts.
Lesson set4 steps7 concepts
函數與變化課程集
Use the functions topic route, the existing graph-first starter track, one accumulation checkpoint, and the calculus topic route so the early math branch stays compact for a teacher-led lesson block.
A sequenced set of 7 concepts.
Lesson set4 steps7 concepts
Vectors to Mechanics Bridge
Use the vectors topic route, the short bridge track, one endpoint checkpoint, and the mechanics topic route so the math-to-motion handoff stays compact and teacher-usable.
A sequenced set of 7 concepts.
Lesson set4 steps9 concepts
Complex and Parametric Motion Lesson Set
Use the complex-and-parametric topic route, the authored starter track, one parametric-motion checkpoint, and the vectors topic route so the plane-based math branch stays compact and teacher-usable.
A sequenced set of 9 concepts.
Lesson set4 steps6 concepts
Rates and Equilibrium Lesson Set
Use the chemistry topic route, the compact starter track, one rebalance checkpoint, and the solutions-and-pH topic route so the chemistry branch feels packaged instead of isolated.
A sequenced set of 6 concepts.
Lesson set4 steps7 concepts
Stoichiometry and Yield Lesson Set
Use the stoichiometry topic route, the compact starter track, one percent-yield checkpoint, and the solutions-and-pH topic route so chemistry quantities stay bounded and teacher-usable.
A sequenced set of 7 concepts.
Lesson set4 steps6 concepts
Solutions and pH Lesson Set
Use the solutions-and-pH topic route, the authored starter track, one buffer checkpoint, and the rates-and-equilibrium topic route so the broader chemistry branch stays compact and teacher-usable.
A sequenced set of 6 concepts.
Playlist4 steps6 concepts
演算法與搜尋播放清單
Use the algorithms-and-search topic route, the compact starter track, one focused graph-traversal revisit, and the filtered challenge hub so the CS branch stays bounded and extension-ready.
A sequenced set of 6 concepts.
Topics
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Open these when you want the library grouped by topic first.
Topics
Show topic pages
Open these when you want the library grouped by topic first.
Topic directory
Open topic directoryTopicPhysics12 concepts
振盪與波動
從單一振子一路連到行進波、聲波、拍頻、都卜勒效應、駐波與共振。
簡諧 is still the cleanest first concept here.
TopicPhysics15 concepts
力學
用向量、轉動、軌跡、重力場、軌道與碰撞在同一套模擬語言中理解運動。
向量 is still the cleanest first concept here.
TopicPhysics5 concepts
流體
從壓力出發，連到靜水壓、連續方程、伯努力原理、浮力與終端速度。
Pressure in fluids is still the cleanest first concept here.
TopicPhysics4 concepts
熱力學
把溫度、內能、理想氣體、熱傳與相變化放在同一條熱學路線中理解。
Temperature vs U is still the cleanest first concept here.
TopicPhysics6 concepts
電學
從電場與電位進到簡單電路、功率、支路行為與等效電阻。
電場 is still the cleanest first concept here.
TopicPhysics5 concepts
電磁學
Use current-made magnetic fields, changing flux, Maxwell's four-law synthesis, magnetic force, and field-pair propagation without turning the branch into a detached rule list.
B-fields is still the cleanest first concept here.
TopicPhysics10 concepts
Optics
Use one bounded optics path to move from light's wave identity into polarization, diffraction, double-slit interference, refraction, prism dispersion, critical angles, mirrors, thin-lens image formation, and the diffraction limits that cap real resolution.
Light and spectrum is still the cleanest first concept here.
TopicPhysics5 concepts
現代物理
Keep the modern-physics branch bounded with the photoelectric effect, atomic spectra, de Broglie matter waves, the Bohr model, and radioactivity / half-life so threshold emission, discrete lines, matter wavelength, quantized hydrogen levels, and probabilistic nuclear decay all stay tied to compact, visually honest benches instead of detached historical anecdotes.
Photoelectric effect is still the cleanest first concept here.
TopicMath3 concepts
函數
Use parent-curve moves, a shifted reciprocal family, and one exponential bench so graph moves, asymptotes, domain breaks, growth versus decay, and target-time questions stay tied to the same visual branch before the math path widens into local and accumulated change.
圖像變換 is still the cleanest first concept here.
TopicMath4 concepts
微積分
Start from slope on the graph itself, use one constrained rectangle bench to make a real maximum visible, keep limit and continuity behavior available on one target point, and then widen into signed area and accumulation so rate and total change stay connected on one visual branch.
Derivative as slope is still the cleanest first concept here.
TopicMath3 concepts
向量
Use one 2D plane to read vectors as arrows, ordered pairs, matrix actions, alignment measures, and projections before the same language bridges into motion.
2D vectors is still the cleanest first concept here.
TopicMath6 concepts
複數與參數運動
Use one bounded math branch where the complex plane, unit-circle rotation, polar coordinates, trig identities, inverse-angle reasoning, and motion traced from equations all stay tied to the same coordinate language.
複數 is still the cleanest first concept here.
TopicChemistry2 concepts
反應速率與平衡
Use one compact chemistry branch where collision success explains reaction rate first, then the same particle language widens into reversible change and a new equilibrium mix.
Reaction rate is still the cleanest first concept here.
TopicChemistry3 concepts
化學計量與產率
Use one compact chemistry branch where a visible recipe bench connects stoichiometric ratios, limiting reagent, and percent yield without leaving the same particle-and-recipe language.
Recipe ratios is still the cleanest first concept here.
TopicChemistry4 concepts
溶液與 pH
Use one compact chemistry branch where concentration, solubility, acid-base balance, buffers, and pH all stay attached to the same bounded solution story.
Concentration is still the cleanest first concept here.
TopicComputer Science6 concepts
演算法與搜尋
Use one bounded CS branch where visible list work grows into one coherent graph-traversal bench, so sorting, binary search, adjacency, BFS, DFS, and visited-state behavior stay on compact live surfaces.
Sorting trade-offs is still the cleanest first concept here.